System and method for controlling the operating area of an inverter coupled to an alternative energy source

ABSTRACT

A system includes a controller programmed to control an inverter to supply a power grid with a maximum amount AC electrical power while operating within an operating area that is pre-defined based on hardware limitations of the inverter. The system allows the inverter to operate with a variable low-DC voltage input into the inverter as opposed to a preset threshold DC voltage, thereby maximizing the amount of power the inverter supplies to a power grid. The inverter controller operates by prioritizing the reactive power output by the inverter over the active power output by the inverter so that the inverter is able to generate an output that meets the reactive power command from a utility and supplies the maximum amount of active power.

BACKGROUND OF THE INVENTION

The present invention relates generally to inverter control systems and,more particularly, to a system and method for controlling an inverter tooperate within a safe operating area while maximizing a power outputfrom an alternative energy source such as, for example, a photovoltaic(PV) array, to a power grid.

Most homes and/or facilities with electrical systems receive alternatingcurrent (AC) electrical power from a utility power grid. Many facilitiesconnected to utility power grids will substitute power from the powergrids with power from their own alternative energy sources. Thealternative energy sources may include solar, wind, geothermal, and/orhydroelectric energy sources, as non-limiting examples. In some cases,the alternative energy sources will generate power in excess of what thefacilities need to operate the facilities' electrical systems. In thosecases, the excess generated electrical power from the alternative energysources can be supplied back into power grids in exchange forcompensation.

Since power grids provide AC electrical power, only AC power can besupplied into power grids. Therefore, in the case of alternative energysources that produce direct current (DC) power, an inverter must be usedto invert the energy from the DC alternative energy sources from DCpower to AC power. An inverter is operated by a controller thatselectively controls switches of the inverter to invert the DC powerinto AC power. During operation, the inverter controller receives areactive power command from a utility and a power grid voltage from thepower grid to which the inverter supplies power. The controller thenregulates switching within the inverter to supply that reactive powerand voltage to the power grid.

These inverters are controlled to limit the input DC-side current andthe output AC-side current so as not to damage the internal hardware ofthe inverter. The operation of an inverter is also restricted by the DCvoltage of the alternative energy source. Typically, the controller foran alternative energy source inverter is designed to switch off theinverter if the DC voltage of the alternative energy source drops belowa preset threshold DC voltage. Therefore, when the DC voltage of thealternative energy source drops below the threshold, no active orreactive power is supplied to the power grid. Further, the reactivepower specified for an inverter is limited to a small percentage of theapparent power rating of the inverter (for example, an inverter may berestricted to providing a power factor of +/−0.91). All of the abovelimitations—the inverter DC and AC current limits, the reactive powercommand and the power grid voltage, the alternative energy source DCvoltage, and the inverter power factor limits—impose restrictions onextracting the maximum amount of active power out of alternative energysources.

The above limitations pose additional restrictions when the inverter isused for higher apparent power applications. Because an inverter haslimited AC current capabilities, the AC voltage of the inverter must beincreased to increase the apparent power rating of the inverter.However, the DC voltage supplied to the inverter from the alternativeenergy source remains the same. This increase in the AC voltage of theinverter makes the problem of low DC voltage more severe because theinverter must be disconnected from the alternative energy source at ahigher DC voltage, further limiting the inverter from extracting activepower from the alternative energy source and supplying the requestedreactive power to the power grid.

In any case, a preset (static) threshold DC voltage limits an inverterfrom providing any power to a power grid when the DC voltage generatedby the alternative energy source is below that threshold DC voltage.Therefore, even if the alternative energy source has a DC voltage outputthat could be used to provide power to the power grid, the inverter willbe switched off if the DC voltage is below the threshold.

It would therefore be desirable to provide a system and method forcontrolling an inverter to operate within the hardware limitations ofthe inverter and the limitations of a power grid while maximizing theactive power provided to the power grid from an alternative energysource under low-DC voltage conditions.

BRIEF DESCRIPTION OF THE INVENTION

Embodiments of the present invention provide a system and method forcontrolling an inverter to operate within its hardware limitations whilemaximizing the supply of active power from an alternative energy sourceto a power grid.

In accordance with one aspect of the invention, a system for controllingan inverter to supply power from a DC power source to a power gridincludes a sensor system coupled to the power grid, a voltage sensorcoupled to an output of the DC power source, and a controller coupled tothe sensor system and the voltage sensor to receive signals therefrom.The controller is programmed to calculate a maximum reactive power thatthe inverter can deliver to the power grid according to a reactive poweralgorithm and based on a reactive power command received from a utility,a power grid voltage received from the sensor system, and a voltage ofthe DC power source received from the voltage sensor. The controller isalso programmed to calculate a maximum active power that the invertercan deliver to the power grid according to an active power algorithm andbased on the maximum reactive power. The controller is furtherprogrammed to control the inverter to deliver to the power grid themaximum reactive power and an active power equal to the smaller of themaximum active power and a maximum power point tracking active powercommand.

In accordance with another aspect of the invention, a method forcontrolling an inverter includes receiving a reactive power command froma utility and sensing a voltage of the power grid and a direct current(DC) voltage of a power source providing power to the power grid. Themethod also includes calculating in a reactive power algorithm a maximumreactive power the inverter can deliver to the power grid based on thereactive power command, the voltage of the power grid, and the DCvoltage of the power source. The method further includes calculating inan active power algorithm a maximum active power the inverter candeliver to the power grid based on the reactive power the inverter candeliver to the power grid. In addition, the method includes outputtingthe maximum reactive power to an inverter current control block andoutputting control signals from the inverter current control block toswitches of the inverter to control the inverter to output to the powergrid the maximum reactive power.

In accordance with yet another aspect of the invention, a photovoltaic(PV) system includes a PV array, an inverter coupled to the PV array forconverting a direct current (DC) voltage of the PV array to analternating current (AC) voltage for delivery to a power grid, a powergrid sensor system for monitoring a voltage of the power grid, and a PVsensor for monitoring the DC voltage of the PV array. The PV system alsoincludes a controller programmed to calculate a maximum reactive powerthe inverter can deliver to the power grid based on a reactive powercommand received from a utility, the voltage of the power grid, the DCvoltage of the PV array, and an AC-side current limit of the inverter.The controller is further programmed to calculate a maximum active powerthe inverter can deliver to the power grid based on the maximum Q-axiscurrent and the AC-side current limit of the inverter. The controller isadditionally programmed to control the inverter to output to the powergrid the maximum reactive power and an active power equal to the lesserof the maximum active power and a maximum power point tracking activepower command.

Various other features and advantages of the present invention will bemade apparent from the following detailed description and the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate preferred embodiments presently contemplated forcarrying out the invention.

In the drawings:

FIG. 1 is a schematic diagram of a photovoltaic (PV) system, accordingto an embodiment of the invention.

FIG. 2 is a flow chart setting forth exemplary steps of the reactivepower algorithm of FIG. 1, according to an embodiment of the invention.

FIG. 3 is a flow chart setting forth exemplary steps of the active poweralgorithm of FIG. 1, according to an embodiment of the invention.

FIG. 4 is a graph illustrating examples of the active and reactive powerachievable in the PV system of FIG. 1, according to an embodiment of theinvention.

FIG. 5 is a series of graphs illustrating a simulation of the PV systemof FIG. 1, according to an embodiment of the invention.

FIG. 6 is a series of graphs illustrating an additional simulation ofthe PV system of FIG. 1, according to an embodiment of the invention.

FIG. 7 is a graph illustrating an example of the active power achievablein the PV system of FIG. 1 as compared to prior art PV systems.

DETAILED DESCRIPTION

Embodiments of the invention relate to a system and method forcontrolling an inverter to supply a utility power grid with the maximumamount AC electrical power while operating within an operating area thatis pre-defined based on hardware limitations of the inverter, namely theDC-side and AC-side current limits of the inverter. This pre-definedoperating area is referred to hereafter as the safe operating area (SOA)of the inverter. Embodiments of the system and method disclosed hereindiffer from prior art systems by allowing the inverter to operate with avariable low-DC voltage input into the inverter instead of using apreset threshold DC voltage, thereby maximizing the amount of power theinverter supplies to a power grid. The inverter controller or controlsystem operates by prioritizing the Q-axis current over the D-axiscurrent so that the inverter is able to generate an output that meetsthe reactive power setting or command from a utility with the maximumamount of active power. While embodiments of the invention are describedherein with reference to a PV system, those with skill in the art willunderstand that the concepts disclosed herein may be used with anyenergy source that generates DC power, including wind, hydro,battery-storage, and flywheel power systems as non-limiting examples.

Referring to FIG. 1, a PV system 10 is illustrated, according to anembodiment of the invention. The PV system 10 includes a PV array 12that supplies a DC voltage, V_(dc), to a DC bus 14. In one embodiment,PV array 12 is composed of a plurality of PV strings (not shown)connected in parallel, with each of the PV strings including a pluralityof modules (not shown) therein that are connected in series to generatea DC power from received solar radiation. While PV system 10 is shownhaving only one PV array 12, it is contemplated that the number of PVarrays in PV system 10 can vary, with two, three, four or more PV arrays12 being included in PV system 10, for example, with each PV array 12being configured to generate a DC power responsive to received solarradiation. Each PV array 12 is composed of a plurality of PV strings(not shown) connected in parallel, with each of the PV strings includinga plurality of modules (not shown) therein that are connected in seriesto generate a DC power.

A capacitor bank 16 having a capacitance C and a three-phase inverter 18are coupled to the DC bus 14 in parallel with the PV array 12. Thecapacitor bank 16 may include one or more capacitors. The inverter 18includes switches or switching elements 20, 22, 24, 26, 28, 30 that areselectively controlled such that inverter 18 outputs a desired AC powerto a utility power grid 50 (including individual phases 44, 46 and 48).Switches 20, 22, 24, 26, 28, 30 may be in the form of any of a number ofvarious switching elements or devices, including a relay, an IGBT, anSCR, a circuit breaker, sub-arrays of small contactors, or othersuitable switching devices. An LC filter 31 including filter inductors32, 34, 36 and filter capacitors 33, 35, 37 is coupled to the inverter18. The inductors 32, 34, 36 are coupled to nodes 38, 40, 42 betweenswitches 20 and 24, 24 and 26, and 28 and 30, respectively, and each ofthe inductors 32, 34, 36 has the same or substantially the sameinductance L. Each inductor 32, 34, 36 is coupled to a phase 44, 46, 48of the utility power grid 50. The capacitors 33, 35, 37 are coupled in aY-configuration to form a low-pass filter. According to variousembodiments of the invention, PV system 10 may also include any numberof additional components (not shown) such as, for example, filters,fuses, contactors, and/or circuit breakers coupled between the inverter18 and the utility power grid 50.

The relationship between the current flowing through the inductors 32,34, 36; the capacitors 33, 35, 37; and the power grid 50 is given by:

I _(L) =I _(C) +I _(grid)  [Eqn. 1],

where I_(L) is the current output by the inverter 18 and flowing throughthe inductors 32, 34, 36; I_(C) is the current flowing through thefilter capacitors 33, 35, 37; and I_(grid) is the current flowing intothe power grid 50. The inverter current, I_(L), splits into the filtercapacitor current, I_(C), and the power grid current, I_(grid), at nodes39, 41, 43. With reference to FIGS. 2-3 and 5-6, various forms of theinverter current, I_(L), the filter capacitor current, I_(C), and thepower grid current, I_(grid), are be labeled to as I_(L) _(_) _(x),I_(C) _(_) _(x), I_(grid) _(_) _(x), with “x” being replaced by theappropriate label.

The PV system 10 also includes an inverter controller or control system52 for controlling the switches 20, 22, 24, 26, 28, 30 of the inverter18. The controller 52 includes two control blocks: an inverter safeoperating area (ISOA) control block 54 and an inverter current controlblock 56. The ISOA control block 54 includes two algorithms: a reactivepower algorithm 58 and an active power algorithm 60. The reactive poweralgorithm 58 receives three inputs: a power grid root mean square (rms)voltage, V_(grid) _(_) _(rms), of the power grid 50 measured at theoutput terminal of the inverter 18 by a sensor system 62, a reactivepower command, Q_(cmd), received from a utility 63, and the PV array DCvoltage, V_(dc), measured by a sensor 64. In various embodiments, thesensor system 62 includes a first sensor (not shown) for sensing thepower grid rms voltage, V_(grid) _(_) _(rms), and a second sensor (notshown) for sensing the grid currents. While the reactive power command,Q_(cmd), is received from the utility 63, a reactive power, Q, fordelivery to the power grid 50 by the inverter 18 is calculated by thereactive power algorithm 58. The reactive power algorithm 58 uses thepower grid rms voltage, V_(grid) _(_) _(rms), the power grid reactivepower command, Q_(cmd), and the PV array DC voltage, V_(dc), tocalculate an inverter Q-axis reference current, I_(q) _(_) _(ref), whichthe reactive power algorithm 58 outputs to the inverter current controlblock 56. The inverter Q-axis reference current, I_(q) _(_) _(ref),represents the maximum Q-axis current the inverter 18 can deliver to thepower grid 50 while staying within the hardware limitations of theinverter 18 and meeting the constraints of the power grid rms voltage,V_(grid) _(_) _(rms), and the PV array DC voltage, V_(dc).

The active power algorithm 60 receives from the reactive power algorithm58 various inputs 68 that will be described further with respect to FIG.2 below. The active power algorithm 60 uses inputs 68 to calculate aninverter D-axis reference current, I_(d) _(_) _(ref), which the activepower algorithm 60 outputs to the inverter current control block 56. Theinverter D-axis reference current, I_(d) _(_) _(ref), represents themaximum possible D-axis current the inverter 18 can deliver to the powergrid 50 while staying within the hardware limitations of the inverter 18and meeting the constraints of the power grid rms voltage, V_(grid) _(_)_(rms), and the PV array DC voltage, V_(dc).

Controller 52 further includes a maximum power point tracking (MPPT)algorithm 72 that calculates an MPPT active power command, P_(cmd),which the MPPT algorithm 72 outputs to the active power algorithm 60 forcalculating the inverter D-axis reference current, I_(d) _(_) _(ref) Theinverter current control block 56 receives the inverter Q-axis andD-axis reference currents, I_(q) _(_) _(ref), I_(d) _(_) _(ref), fromreactive power and active power algorithms 58, 60 and selectivelycontrols switches 20, 22, 24, 26, 28, 30 of the inverter 18 to supplythe maximum possible Q-axis and D-axis currents the inverter 18 candeliver to the power grid 50 while staying within the hardwarelimitations of the inverter 18 and meeting the constraints of the powergrid rms voltage, V_(grid) _(_) _(rms), and the PV array DC voltage,V_(dc).

Referring now to FIG. 2, the reactive power algorithm 58 of FIG. 1 forcalculating the inverter Q-axis reference current, I_(q) _(_) _(ref), isset forth, according to an embodiment of the invention. The reactivepower algorithm 58 is based on defining an operating range of theinverter 18 based on a maximum voltage at the AC-side terminal of theinverter 18. The reactive power algorithm 58 starts at STEP 76 when thecontroller 52 is powered on. At STEP 78, the reactive power algorithm 58receives the power grid rms voltage, V_(grid) _(_) _(rms) (FIG. 1), thepower grid reactive power command, Q_(cmd), and the PV array DC voltage,V_(dc).

At STEP 80, the reactive power algorithm 58 calculates a power gridD-axis voltage, V_(grid) _(_) _(d), which is the D-axis voltagecomponent of the power grid rms voltage, V_(grid) _(_) _(rms), of thepower grid 50. The reactive power algorithm 58 calculates the power gridD-axis voltage, V_(grid) _(_) _(d), according to:

$\begin{matrix}{{V_{grip\_ d} = {V_{grid\_ rms} \cdot \frac{\sqrt{2}}{\sqrt{3}} \cdot {kref}}},} & \left\lbrack {{Eqn}.\mspace{14mu} 2} \right\rbrack\end{matrix}$

where kref is a reference constant set to a specific value based onrepresentations of the various D-axis and Q-axis currents and voltagesused in the reactive power algorithm 58 and the active power algorithm60. In one embodiment, the reference constant, kref, is set to 1.5 forcalculating three-phase representations of the various D-axis and Q-axisvoltages and currents. In other embodiments, the various D-axis andQ-axis voltages and currents are calculated using other representations.As one non-limiting example, the reference constant, kref, is 1 insteadof 1.5.

At STEP 82, the reactive power algorithm 58 calculates a powergrid-requested Q-axis current, I_(grid) _(_) _(q) _(_) _(requested),according to:

$\begin{matrix}{{I_{{grid\_ q}{\_ requested}} = {{kref} \cdot 1000 \cdot \frac{Q_{cmd}}{- V_{grid\_ d}}}},} & \left\lbrack {{Eqn}.\mspace{14mu} 3} \right\rbrack\end{matrix}$

where the power grid-requested Q-axis current, I_(grid) _(_) _(q) _(_)_(requested), represents the Q-axis current that the inverter 18 needsto supply to the power grid 50 with the power grid D-axis voltage,V_(grid) _(_) _(d), to supply the power grid reactive power command,Q_(cmd), to the power grid 50.

At STEP 84, the reactive power algorithm 58 calculates a filtercapacitor Q-axis current, I_(C) _(_) _(q), according to:

$\begin{matrix}{{I_{C\_ q} = \frac{V_{grid\_ d}}{X_{C\_ q}}},} & \left\lbrack {{Eqn}.\mspace{14mu} 4} \right\rbrack\end{matrix}$

where X_(C) _(_) _(q) is a capacitive reactance of the filter capacitors33, 35, 37. The filter capacitor Q-axis current, I_(C) _(_) _(q),represents the Q-axis current flowing into the filter capacitors 33, 35,37 of the LC filter 31. At STEP 86, the reactive power algorithm 58calculates a power grid-requested inverter Q-axis current, I_(L) _(_)_(q) _(_) _(requested), according to:

I _(L) _(_) _(q) _(_) _(requested) =I _(grid) _(_) _(q) _(_)_(requested) +I _(C) _(_) _(q)  [Eqn. 5],

where the power grid-requested inverter Q-axis current, I_(L) _(_) _(q)_(_) _(requested), represents the current flowing through the inductors32, 34, 36 corresponding to the total of the power grid-requested Q-axiscurrent, I_(grid) _(_) _(q) _(_) _(requested), and the filter capacitorQ-axis current, I_(C) _(_) _(q).

At STEP 88, the reactive power algorithm 58 calculates a maximuminverter peak AC voltage, V_(invpeak) _(_) _(max), of the inverter 18according to:

$\begin{matrix}{{V_{invpeak\_ max} = {V_{{inv\_ d}{\_ max}} = {{ksf} \cdot {kpwm} \cdot \frac{V_{dc}}{2}}}},} & \left\lbrack {{Eqn}.\mspace{14mu} 6} \right\rbrack\end{matrix}$

where ksf is a safety factor applied to give a safety margin on themaximum inverter peak AC voltage, V_(invpeak) _(_) _(max), to ensure nodamage is done to the inverter 18 and kpwm represents a percentageincrease in voltage achieved due to 3rd harmonic injection that willvary based on what pulse width modulation (PWM) technique is used tocontrol the inverter 18. For example, kpwm may be set to 1.15 for onePWM technique to represent a 15% increase in voltage due to 3rd harmonicinjection. The maximum inverter peak AC voltage, V_(invpeak) _(_)_(max), is a theoretical maximum peak voltage on the AC-side of theinverter 18 based on the PV array DC voltage, V_(dc), on the DC-side ofthe inverter 18. Exemplary, non-limiting values of the safety factor,ksf, may include 0.99 (99% of the maximum inverter peak AC voltage,V_(invpeak) _(_) _(max)) and 0.98 (98% of the maximum inverter peak ACvoltage, V_(invpeak) _(_) _(max)).

At STEP 90, the reactive power algorithm 58 calculates a minimumallowable inverter Q-axis current, I_(L) _(_) _(q) _(_) _(allowed),according to:

$\begin{matrix}{{I_{{L\_ q}{\_ allowed}} = \frac{- \left( {{{kref} \cdot V_{{inv\_ d}{\_ max}}} - V_{grid\_ d}} \right)}{\left( {\omega \cdot L} \right)}},} & \left\lbrack {{Eqn}.\mspace{14mu} 7} \right\rbrack\end{matrix}$

where ω is an angular frequency of the PV system 10. The minimumallowable inverter Q-axis current, I_(L) _(_) _(q) _(_) _(allowed), isthe Q-axis current that would flow through the inductors 32, 34, 36 ifthe inverter 18 outputs the maximum inverter peak AC voltage, V_(inv)_(_) _(d) _(_) _(max).

At STEP 92, the reactive power algorithm 58 calculates an inverterQ-axis current, I_(L) _(_) _(q) _(_) _(delivered), for delivery by theinverter 18 according to:

if(I _(L) _(_) _(q) _(_) _(requested) <I _(L) _(_) _(q) _(_) _(allowed))

I _(L) _(_) _(q) _(_) _(delivered) =I _(L) _(_) _(q) _(_) _(allowed)

Else

I _(L) _(_) _(q) _(_) _(delivered) =I _(L) _(_) _(q) _(_)_(requested)  [Eqn. 8],

where I_(L) _(_) _(q) _(_) _(delivered) is the current the inverter 18should deliver to the inductors 32, 34, 36. As shown by Eqn. 8, thereactive power algorithm 58 will not allow the inverter Q-axis current,I_(L) _(_) _(q) _(_) _(delivered), to be set to a value less than thevalue of the minimum allowable inverter Q-axis current, I_(L) _(_) _(q)_(_) _(allowed), so the inverter 18 is not damaged. At STEP 94, thereactive power algorithm 58 calculates a raw value for a power gridQ-axis current, I_(grid) _(_) _(q) _(_) _(delivered) _(_) _(raw), fordelivery to the power grid 50 by the inverter 18 corresponding to theinverter Q-axis current, I_(L) _(_) _(q) _(_) _(delivered), accordingto:

I _(grid) _(_) _(q) _(_) _(delivered) _(_) _(raw) =I _(L) _(_) _(q) _(_)_(delivered) −I _(C) _(_) _(q)  [Eqn. 9],

where I_(grid) _(_) _(q) _(_) _(delivered) _(_) _(raw) is the value ofthe Q-axis current the power grid 50 would receive if inverter 18outputs the inverter Q-axis current, I_(L) _(_) _(q) _(_) _(delivered).

At STEP 96, the reactive power algorithm 58 calculates a power gridQ-axis current, I_(grid) _(_) _(q) _(_) _(delivered), for delivery tothe power grid 50 by the inverter 18 according to:

if(I _(grid) _(_) _(q) _(_) _(delivered) _(_) _(raw) <−kref·1.414·I_(ac) _(_) _(lim))

I _(grid) _(_) _(q) _(_) _(delivered) =−kref·1.414·I _(ac) _(_) _(lim)

else if(I _(grid) _(_) _(q) _(_) _(delivered) _(_) _(raw) >kref·1.414·I_(ac) _(_) _(lim))

I _(grid) _(_) _(q) _(_) _(delivered) =kref·1.414·I _(ac) _(_) _(lim)

I _(grid) _(_) _(q) _(_) _(delivered) =I _(grid) _(_) _(q) _(_)_(delivered) _(_) _(raw)  [Eqn. 10],

where I_(ac) _(_) _(lim) is an AC-side rms current limit of the inverter18 and I_(grid) _(_) _(q) _(_) _(delivered) is the Q-axis current thatshould be delivered to the power grid 50. As shown by Eqn. 10, thereactive power algorithm 58 will not allow the power grid Q-axiscurrent, I_(grid) _(_) _(q) _(_) _(delivered), to be set to a valuebeyond the negative or positive value of the AC-side rms current limit,I_(ac) _(_) _(lim), of the inverter 18 so that the inverter 18 operateswithin its SOA. Therefore, the power grid Q-axis current, I_(grid) _(_)_(q) _(_) _(delivered), is the maximum possible Q-axis current theinverter 18 can output while operating within its SOA and meeting theconstraints of the PV array DC voltage, V_(dc), and the power grid rmsvoltage, V_(grid) _(_) _(rms).

At STEP 98, the reactive power algorithm 58 calculates the reactivepower, Q, for delivery to the power grid 50 by the inverter 18 accordingto:

$\begin{matrix}{Q = {{- V_{grid\_ d}} \cdot I_{{grid\_ q}{\_ delivered}} \cdot {\frac{1}{kref}.}}} & \left\lbrack {{Eqn}.\mspace{14mu} 11} \right\rbrack\end{matrix}$

Since the reactive power algorithm 58 uses the power grid Q-axiscurrent, I_(grid) _(_) _(q) _(_) _(delivered), to calculate the reactivepower, Q, the reactive power, Q, is the maximum possible reactive powerthe inverter 18 can output while operating within its SOA and meetingthe constraints of the PV array DC voltage, V_(dc), and the power gridrms voltage, V_(grid) _(_) _(rms). At STEP 100, the reactive poweralgorithm 58 calculates Q-axis reference current, I_(q) _(_) _(ref),according to:

$\begin{matrix}{{I_{q\_ ref} = \frac{Q}{Q_{pu} \cdot 1000}},} & \left\lbrack {{Eqn}.\mspace{14mu} 12} \right\rbrack\end{matrix}$

where Q_(pu) is a preset reactive power constant corresponding tocharacteristics of the inverter 18 used to calculate Q-axis referencecurrent, I_(q) _(_) _(ref), from reactive power, Q.

STEPS 102 and 104 of the reactive power algorithm 58 are performedsimultaneously. At STEP 102, the reactive power algorithm 58 outputs thepower grid D-axis voltage, V_(grid) _(_) _(d), the maximum inverter peakAC voltage, V_(invpeak) _(_) _(max), and the power grid Q-axis current,I_(grid) _(_) _(q) _(_) _(delivered), for delivery to the power grid 50by the inverter 18 to the active power algorithm 60. In anotherembodiment, the reactive power algorithm 58 outputs the power gridD-axis voltage, V_(grid) _(_) _(d), the maximum inverter peak ACvoltage, V_(invpeak) _(_) _(max), and the power grid Q-axis current,I_(grid) _(_) _(q) _(_) _(delivered), to the active power algorithm 60as each is calculated by the reactive power algorithm 58. At STEP 104,the reactive power algorithm 58 outputs the inverter Q-axis referencecurrent, I_(q) _(_) _(ref), to the inverter current control block 56,which interprets the Q-axis reference current, I_(q) _(_) _(ref), andoutputs signals to switches 20, 22, 24, 26, 28, 30 of the inverter 18 sothat the inverter 18 outputs the power grid Q-axis current I_(grid) _(_)_(q) _(_) _(delivered).

Referring now to FIG. 3, the active power algorithm 60 of FIG. 1 forcalculating the inverter D-axis reference current, I_(d) _(_) _(ref), isset forth, according to an embodiment of the invention. The reactivepower algorithm 58 starts at STEP 106 when the controller 52 is poweredon. At STEP 108, the active power algorithm 60 receives the power gridD-axis voltage, V_(grid) _(_) _(d), the maximum inverter peak ACvoltage, V_(invpeak) _(_) _(max), and the power grid Q-axis current,I_(grid) _(_) _(q) _(_) _(delivered), from the reactive power algorithm58. At STEP 110, the active power algorithm 60 calculates a new valuefor the inverter Q-axis current, I_(L) _(_) _(q) _(_) _(delivered), fordelivery by the inverter 18 according to:

I _(L) _(_) _(q) _(_) _(delivered) =I _(grid) _(_) _(q) _(_)_(delivered) +I _(C) _(_) _(q)  [Eqn. 13].

Although the inverter Q-axis current, I_(L) _(_) _(q) _(_) _(delivered),has already been calculated in the reactive power algorithm 58 in Eqn.8, the inverter Q-axis current, I_(L) _(_) _(q) _(_) _(delivered),through the inductors 32, 34, 36 is recalculated in the active poweralgorithm 60 in Eqn. 13 using the power grid Q-axis current, I_(grid)_(_) _(q) _(_) _(delivered), as opposed to the raw value of the powergrid Q-axis current, I_(grid) _(_) _(q) _(_) _(delivered) _(_) _(raw),in Eqn. 9. In this manner, Eqn. 13 accounts for the situation when thepower grid Q-axis current, I_(grid) _(_) _(q) _(_) _(delivered), is setto a value other than the raw value of the power grid Q-axis current,I_(grid) _(_) _(q) _(_) _(delivered) _(_) _(raw), in Eqn. 10 because ofthe AC-side rms current limit, I_(ac) _(_) _(lim).

At STEP 112, the active power algorithm 60 calculates an inductor D-axisvoltage drop, V_(L) _(_) _(d), across inductors 32, 34, 36 correspondingto the inverter Q-axis current, I_(L) _(_) _(q) _(_) _(delivered),according to:

V _(L) _(_) _(d) =−I _(L) _(_) _(q) _(_) _(delivered) ·ω·L  [Eqn. 14].

At STEP 114, the active power algorithm 60 calculates an inverter D-axisvoltage, V_(inv) _(_) _(d), for delivery by the inverter 18 accordingto:

V _(inv) _(_) _(d) =V _(grid) _(_) _(d) +V _(L) _(_) _(d)  [Eqn. 15],

where the inverter D-axis voltage, V_(inv) _(_) _(d), represents thevoltage output by the inverter 18 corresponding to the total of thepower grid D-axis voltage, V_(grid) _(_) _(d), and the inductor D-axisvoltage drop, V_(L) _(_) _(d). The inverter D-axis voltage, V_(inv) _(_)_(d), is the D-axis voltage the inverter 18 needs to output to supplythe power grid reactive power command, Q_(cmd). At STEP 116, the activepower algorithm 60 calculates an inverter Q-axis voltage, V_(inv) _(_)_(q), for delivery by the inverter 18 corresponding to the inverter peakAC voltage, V_(invpeak) _(_) _(max), and the inverter D-axis voltage,V_(inv) _(_) _(d), according to:

V _(inv) _(_) _(q)=√{square root over (((kref·V _(invpeak) _(_) _(max))²−V _(inv) _(_) _(d) ²))}  [Eqn. 16].

At STEP 118, the active power algorithm 60 calculates a maximumallowable inverter D-axis current, I_(L) _(_) _(d) _(_) _(max),corresponding to the inverter Q-axis voltage, V_(inv) _(_) _(q),according to:

$\begin{matrix}{I_{{L\_ d}{\_ max}} = {\frac{V_{inv\_ q}}{\left( {\omega \cdot L} \right)}.}} & \left\lbrack {{Eqn}.\mspace{14mu} 17} \right\rbrack\end{matrix}$

The maximum allowable inverter D-axis current, I_(L) _(_) _(d) _(_)_(max), represents a maximum allowed active power the inverter 18 canoutput and remain in its SOA. At STEP 120, the active power algorithm 60calculates a commanded maximum inverter D-axis current, I_(L) _(_) _(d)_(_) _(cmd) _(_) _(max), according to:

I _(L) _(_) _(d) _(_) _(cmd) _(_) _(max)=min(√{square root over(((kref·1.414·I _(ac) _(_) _(lim))² −I _(grid) _(_) _(q) _(_)_(delivered) ²))},I _(L) _(_) _(d) _(_) _(max))  [Eqn. 18].

As shown in Eqn. 18, the active power algorithm 60 will not allow thecommanded maximum inverter current, I_(L) _(_) _(d) _(_) _(cmd) _(_)_(max), to be set to a value beyond the AC-side rms current limit,I_(ac) _(_) _(lim), of the inverter 18 so that the inverter 18 operateswithin its SOA.

At STEP 122, the active power algorithm 60 calculates a maximumallowable power grid D-axis current, I_(grid) _(_) _(d) _(_) _(allowed),due to a DC-side current limit of the inverter 18 according to:

$\begin{matrix}{{I_{{grid\_ d}{{\_ allowe}d}} = {\left( {\eta \cdot V_{dc} \cdot I_{{dc}\_ \lim}} \right) \cdot \frac{kref}{V_{{grid}\_ d}}}},} & \left\lbrack {{Eqn}.\mspace{14mu} 19} \right\rbrack\end{matrix}$

where η is the power efficiency of the inverter 18. At STEP 124, theactive power algorithm 60 calculates a power grid D-axis current,I_(grid) _(_) _(d) _(_) _(delivered), for delivery to the power grid 50by the inverter 18 according to:

I _(grid) _(_) _(d) _(_) _(delivered)=min(I _(L) _(_) _(d) _(_) _(cmd)_(_) _(max) ,I _(grid) _(_) _(q) _(_) _(allowed))  [Eqn. 20].

where I_(grid) _(_) _(d) _(_) _(delivered) is the D-axis current thatshould be delivered to the power grid 50. As shown in Eqns. 19 and 20,the active power algorithm 60 will not allow the power grid D-axiscurrent, I_(grid) _(_) _(d) _(_) _(delivered), to be set to a valuebeyond the DC-side current limit of the inverter 18 so that the inverter18 operates within its SOA. Therefore, the power grid D-axis current,I_(grid) _(_) _(d) _(_) _(delivered), is the maximum possible D-axiscurrent the inverter 18 can output while operating within its SOA andmeeting the constraints of the PV array DC voltage, V_(dc), and thepower grid rms voltage, V_(grid) _(_) _(rms).

At STEP 126, the active power algorithm 60 calculates a raw value of theactive power, P, for delivery to the power grid 50 by the inverter 18according to:

$\begin{matrix}{P_{raw} = {{V_{{grid}\_ d} \cdot I_{{grid\_ d}{{\_ delivered} \cdot}}}\frac{1}{kref}}} & \left\lbrack {{Eqn}.\mspace{14mu} 21} \right\rbrack\end{matrix}$

Because the active power algorithm 60 uses the power grid D-axiscurrent, I_(grid) _(_) _(d) _(_) _(delivered), to calculate the rawvalue of the active power, P_(raw), the raw value of the active power,P_(raw), is the maximum possible active power the inverter 18 can outputwhile operating within its SOA and meeting the constraints of the PVarray DC voltage, V_(dc), and the power grid rms voltage, V_(grid) _(_)_(rms). At STEP 128, the active power algorithm 60 calculates the activepower, P, for delivery to the power grid 50 according to:

P=min(P _(raw) ,P _(cmd))  [Eqn. 22].

Therefore, if the raw value of the active power, P_(raw), is less thanthe MPPT active power command, P_(cmd), the active power, P, is limitedby the SOA of the inverter 18. However, if the maximum possible activepower, P_(raw), allowed by the SOA of the inverter 18 is greater thanthe MPPT active power command, P_(cmd), the active power, P, is limitedto the MPPT active power command, P_(cmd).

At STEP 130, the active power algorithm 60 calculates D-axis referencecurrent, I_(d) _(_) _(ref), according to:

$\begin{matrix}{{I_{d\_ {ref}} = \frac{P}{P_{pu} \cdot 1000}},} & \left\lbrack {{Eqn}.\mspace{14mu} 23} \right\rbrack\end{matrix}$

where P_(pu) is a preset active power constant corresponding tocharacteristics of the inverter 18 used to calculate D-axis referencecurrent, I_(d) _(_) _(ref), from the active power, P. At STEP 131, theactive power algorithm 60 outputs the inverter D-axis reference current,I_(d) _(_) _(ref), to the inverter current control block 56, whichinterprets the D-axis reference current, I_(d) _(_) _(ref), and outputssignals to switches 20, 22, 24, 26, 28, 30 of the inverter 18 so thatthe inverter 18 outputs the power grid D-axis current, I_(grid) _(_)_(d) _(_) _(delivered).

Referring now to FIGS. 1-3, because the active power algorithm 60receives inputs from the reactive power algorithm 58 to function, thereactive power algorithm 58 is a priority over the active poweralgorithm 60. In other words, the inverter 18 prioritizes delivery ofthe reactive power to the power grid 50 over the active power. In thismanner, the power grid reactive power command, Q_(cmd), will always bemet by the inverter 18 and the inverter 18 can supply active power tothe power grid 50, even when the PV array DC voltage, V_(dc), drops tolevel where the inverter 18 can no longer supply power according to theMPPT active power command, P_(cmd). However, when the power gridreactive power command, Q_(cmd), is set to zero, the inverter 18operates with no priority to deliver the reactive power, Q, andprioritizes delivery of the active power, P.

Referring now to FIG. 4, an exemplary graph 132 illustrates examples ofthe active and reactive power achievable in the PV system 10, accordingto an embodiment of the invention. Graph 132 illustrates a series offive simulations run in the PV system 10: a first simulation 134, asecond simulation 136, a third simulation 138, a fourth simulation 140,and a fifth simulation 142. In each simulation 134, 136, 138, 140, 142,the power grid rms voltage, V_(grid) _(_) _(rms), is 384 V line-to-line,the DC-side current limit of the inverter 18 is 3100 amperes (A), andthe AC-side current limit of the inverter 18 is 2970 A. Each simulation134, 136, 138, 140, 142 shows the amount of active power, P, inkilowatts (kW) that the inverter 18 can deliver to the power grid 50 fordifferent levels of reactive power, Q, delivered to the power grid 50 bythe inverter 18. The reactive power is displayed in kilovolt-amperesreactive (kVAR) and is varied from −800 kVAR to 800 kVAR. Eachsimulation 134, 136, 138, 140, 142 corresponds to a different PV arrayDC voltage, V_(dc).

In the first simulation 134, the PV array DC voltage is 600 V. As shown,the inverter 18 is able to supply a large amount of the active powerover the entire range of the reactive power. The same can be said of theinverter 18 in the second simulation 136, in which the PV array DCvoltage is 580 V. However, in the third, fourth, and fifth simulations138, 140, 142, in which the PV array DC voltage is 570 V, 560 V, and 550V, respectively, the inverter 18 is not able to supply as much activepower over the entire range of the reactive power.

In the third simulation 138, the inverter 18 cannot supply as muchactive power after the reactive power increases to a level above 600kVAR. Because of the inverter Q-axis and D-axis reference currents I_(q)_(_) _(ref), I_(d) _(_) _(ref), received from the reactive and activepower algorithms 58, 60 of the ISOA control block 54, the invertercurrent control block 56 is able to curtail the amount active power theinverter 18 outputs to the power grid 50. The inverter current controlblock controls the inverter 18 to output as much active power aspossible while still operating within the SOA of the inverter 18 andmeeting the constraints of the power grid rms voltage, V_(grid) _(_)_(rms), and the PV array DC voltage, V_(dc). The same can be said of theinverter 18 in the fourth and fifth simulations 140, 142, except thatthe active power, P, the inverter 18 is able to supply to the power grid50 starts to decrease above 400 kVAR and 200 kVAR, respectively, becauseof the lower PV array DC voltages of 560 V and 550 V, respectively.However, when the power grid reactive power command, Q_(cmd), becomestoo high (above 600 kVAR in the case of the fourth simulation 140 andabove 400 kVAR in the case of the fifth simulation 142), the invertercurrent control block 56 must also curtail the reactive power. When thereactive power is curtailed, the active power is zero.

The controller 52 is able to operate under both capacitive reactivepower conditions (when the reactive power is negative) and inductivereactive power conditions (when the reactive power is positive).However, under capacitive reactive power conditions, the voltage outputby inverter 18 is less than the power grid rms voltage, V_(grid) _(_)_(rms). Therefore, a low PV array DC bus voltage, V_(dc), does notconstrain the operation of the inverter 18 under capacitive reactivepower conditions, and the maximum reactive power is constrained only inthe case of the inductive reactive power conditions.

Referring now to FIG. 5, results of an example simulation 148 run on thePV system 10 are shown, according to an embodiment of the invention. Theresults of the simulation 148 are illustrated by a first graph 150, asecond graph 152, and a third graph 154. The first graph 150 illustratesthe parameters of the simulation 148. In the simulation 148, the PVarray DC voltage, V_(dc), is varied from 550 V to 650 V at a frequencyof 2 hertz (Hz). The power grid reactive power command, Q_(cmd), isvaried from 450 kVAR to 675 kVAR at a frequency of 1 Hz. The secondgraph 152 illustrates the active power, P, for delivery to the powergrid 50 by the inverter 18. The third graph 154 illustrates the reactivepower, Q, for delivery to the power grid 50 by the inverter 18. Thepower grid rms voltage, V_(grid) _(_) _(rms), is set at 384 Vline-to-line.

As seen in the simulation 148, the active power is curtailed wheneverthere is not enough of the PV array DC voltage, V_(dc), to supply theactive power and meet the power grid reactive power command, Q_(cmd).The active power is curtailed around 0.5 seconds, 1 second, and 1.5seconds when the PV array DC voltage, V_(dc), is at 575 V. Thecontroller 52 controls the inverter 18 to output the maximum amount ofactive power without going outside of the SOA of the inverter 18 andmeeting the constraints of the PV array DC voltage, V_(dc), and thepower grid rms voltage, V_(grid) _(_) _(rms). When the reactive powerfor delivery to the power grid 50 by the inverter 18 is also curtailedshortly after 0.5 seconds, 1 second, and 1.5 seconds in the third graph154, the active power drops to 0 V.

Referring now to FIG. 6, results of another example simulation 156 runon the PV system 10 are shown, according to an embodiment of theinvention. The results of the simulation 156 are illustrated by a firstgraph 158, a second graph 160, and a third graph 162. The first graph158 illustrates the parameters of the simulation 156. In the simulation156, the PV array DC voltage, V_(dc), is varied from 550 V to 650 V at afrequency of 2 Hz. The power grid reactive power command, Q_(cmd), isvaried from −800 kVAR to 800 kVAR at a frequency of 0.25 Hz. The secondgraph 160 illustrates the active power, P, for delivery to the powergrid 50 by the inverter 18. The third graph 162 illustrates the reactivepower, Q, delivered to the power grid 50 by the inverter 18. The powergrid rms voltage, V_(grid) _(_) _(rms), was set to 384 V line-to-line.

As seen in the first, second, and third graphs 158, 160, 162, when thepower grid reactive power command, Q_(cmd), is a negative value, almostfull active power is supplied by the inverter 18. The active power isonly curtailed due to the DC-side current limit, I_(dc) _(_) _(limit),of the inverter 18 when the power grid reactive power command, Q_(cmd),is negative. However, the active power is curtailed when the power gridreactive power command, Q_(cmd), is positive and there is not enough ofthe PV array DC voltage, V_(dc), to supply the active power and meet thepower grid reactive power command, Q_(cmd). The controller 52 controlsthe inverter 18 to output the maximum amount of active power withoutgoing outside of the SOA of the inverter 18 and meeting the constraintsof the PV array DC voltage, V_(dc), and the power grid rms voltage,V_(grid) _(_) _(rms). When the reactive power for delivery to the powergrid 50 by the inverter 18 is also curtailed shortly after 0.5 seconds,1 second, and 1.5 seconds in the third graph 162, the active power dropsto 0 V.

Referring now to FIG. 7, an exemplary graph 164 illustrates an exampleof the active power, P, for delivery to power grid 50 by the inverter 18achievable in the PV system 10 versus the active power achievable inprior art PV systems. The graph 164 illustrates the level of activepower in kW for delivery to the power grid 50 for a PV array DC voltage,V_(dc). In the graph 164, the PV array DC voltage decreases to a levelthat is too low for providing full active power at 600 V. An ISOAoperational curve 166 for the PV system 10 illustrates how thecontroller 52 is able to control the inverter 18 to supply some activepower to the power grid, even after there is not enough PV array DCvoltage to supply full active power. As shown, the active power beginsto drop at a PV array DC voltage of 600 V and drops to a value of 0 V ata PV array DC voltage of 550 V when the reactive power, Q, is alsocurtailed.

In contrast with the ISOA operation curve 166, a threshold operationalcurve 168 for a prior art PV system illustrates how the controller shutsdown the inverter at a PV array DC voltage, V_(dc), of 600 V to preventthe inverter from exceeding its DC-side and AC-side current limits.While both the prior art inverter and the inverter 18 are both preventedfrom exceeding their DC-side and AC-side current limits, the inverter 18is able to supply active power, P, at a minimum PV array DC voltage thatis 50 V less than the minimum PV array DC voltage of the prior artinverter. Therefore, controller 52 provides the advantage of allowingthe inverter 18 of the PV system 10 to supply active power to the powergrid 50 for a longer period of time, thereby maximizing the amount ofactive power supplied to the power grid 50 over the lifetime of the PVsystem 10.

Beneficially, embodiments of the invention thus provide a system andmethod of controlling an inverter to supply power to a power grid underlow-DC voltage input conditions. An inverter controller controls theinverter to operate within a SOA defined by the hardware limitations ofthe inverter while still meeting the constraints of a power grid voltageand a power grid reactive power setting or command. The invertercontroller includes an ISOA control block including a reactive poweralgorithm for calculating the maximum Q-axis current (the maximumreactive power) the inverter can supply to the power grid and an activepower algorithm for calculating the maximum D-axis current (the maximumactive power) the inverter can supply to the power grid. An invertercurrent control block receives commands corresponding to the maximumQ-axis and D-axis currents and controls the inverter switches to outputthe maximum Q-axis and D-axis currents, even under low-DC voltage inputconditions. Thus the inverter controller enables the inverter to providethe maximum amount of active power to the power grid under allconditions.

According to one embodiment of the present invention, a system forcontrolling an inverter to supply power from a DC power source to apower grid includes a sensor system coupled to the power grid, a voltagesensor coupled to an output of the DC power source, and a controllercoupled to the sensor system and the voltage sensor to receive signalstherefrom. The controller is programmed to calculate a maximum reactivepower that the inverter can deliver to the power grid according to areactive power algorithm and based on a reactive power command receivedfrom a utility, a power grid voltage received from the sensor system,and a voltage of the DC power source received from the voltage sensor.The controller is also programmed to calculate a maximum active powerthat the inverter can deliver to the power grid according to an activepower algorithm and based on the maximum reactive power. The controlleris further programmed to control the inverter to deliver to the powergrid the maximum reactive power and an active power equal to the smallerof the maximum active power and a maximum power point tracking activepower command.

According to another embodiment of the present invention, a method forcontrolling an inverter includes receiving a reactive power command froma utility and sensing a voltage of the power grid and a direct current(DC) voltage of a power source providing power to the power grid. Themethod also includes calculating in a reactive power algorithm a maximumreactive power the inverter can deliver to the power grid based on thereactive power command, the voltage of the power grid, the DC voltage ofthe power source. The method further includes calculating in an activepower algorithm a maximum active power the inverter can deliver to thepower grid based on the reactive power the inverter can deliver to thepower grid. In addition, the method includes outputting the maximumreactive power to an inverter current control block and outputtingcontrol signals from the inverter current control block to switches ofthe inverter to control the inverter to output to the power grid themaximum reactive power.

According to yet another embodiment of the present invention, aphotovoltaic (PV) system includes a PV array, an inverter coupled to thePV array for converting a direct current (DC) voltage of the PV array toan alternating current (AC) voltage for delivery to a power grid, apower grid sensor system for monitoring a voltage of the power grid, anda PV sensor for monitoring the DC voltage of the PV array. The PV systemalso includes a controller programmed to calculate a maximum reactivepower the inverter can deliver to the power grid based on a reactivepower command received from a utility, the voltage of the power grid,the DC voltage of the PV array, and an AC-side current limit of theinverter. The controller is further programmed to calculate a maximumactive power the inverter can deliver to the power grid based on themaximum Q-axis current and the AC-side current limit of the inverter.The controller is additionally programmed to control the inverter tooutput to the power grid the maximum reactive power and an active powerequal to the lesser of the maximum active power and a maximum powerpoint tracking active power command.

The present invention has been described in terms of the preferredembodiment, and it is recognized that equivalents, alternatives, andmodifications, aside from those expressly stated, are possible andwithin the scope of the appending claims.

What is claimed is:
 1. A system for controlling an inverter to supplypower from a DC power source to a power grid, the system comprising: asensor system coupled to the power grid; a voltage sensor coupled to anoutput of the DC power source; and a controller coupled to the sensorsystem and the voltage sensor to receive signals therefrom, thecontroller programmed to: calculate a maximum reactive power that theinverter can deliver to the power grid according to a reactive poweralgorithm and based on a reactive power command received from a utility,a power grid voltage received from the sensor system, and a voltage ofthe DC power source received from the voltage sensor; calculate amaximum active power that the inverter can deliver to the power gridaccording to an active power algorithm and based on the maximum reactivepower; and control the inverter to deliver to the power grid the maximumreactive power and an active power equal to the smaller of the maximumactive power and a maximum power point tracking active power command. 2.The control system of claim 1 wherein the reactive power algorithmcalculates the maximum reactive power by: calculating a powergrid-requested inverter Q-axis current based on the reactive powercommand and the power grid voltage; calculating a minimum allowableinverter Q-axis current based on the voltage of the power grid and amaximum peak AC voltage of the inverter; calculating an inverter Q-axiscurrent for delivery by the inverter based on the minimum allowableinverter Q-axis current and the power grid-requested inverter Q-axiscurrent; calculating a maximum power grid Q-axis current for delivery tothe power grid based on the inverter Q-axis current for delivery to thepower grid and an AC-side current limit of the inverter; and calculatingthe maximum reactive power based on the maximum power grid Q-axiscurrent.
 3. The control system of claim 2 wherein the reactive poweralgorithm is configured to: calculate a raw value for the maximum powergrid Q-axis current using the inverter Q-axis current for delivery tothe power grid; set the maximum power grid Q-axis current equal to−kref·1.414·I_(ac) _(_) _(lim) if the raw value for the maximum Q-axiscurrent is less than −kref·1.414·I_(ac) _(_) _(lim), where kref is areference constant corresponding to the representation of D-axis andQ-axis currents and voltages and I_(ac) _(_) _(lim) is the AC-sidecurrent limit of the inverter; set the maximum power grid Q-axis currentto kref·1.4141·I_(ac) _(_) _(lim) if the raw value for the maximumQ-axis current is greater than kref·1.414·I_(ac) _(_) _(lim); and setthe maximum power grid Q-axis current to the raw value for the maximumQ-axis current otherwise.
 4. The control system of claim 2 wherein thereactive power algorithm is configured to: set the inverter Q-axiscurrent for delivery to the power grid equal to the minimum allowableinverter Q-axis current if the power grid-requested inverter Q-axiscurrent is less than the minimum allowable inverter Q-axis current; andset the inverter Q-axis current for delivery to the power grid equal tothe power grid-requested inverter Q-axis current requested otherwise. 5.The control system of claim 2 wherein the reactive power algorithmcalculates the maximum peak AC voltage of the inverter using a safetyfactor.
 6. The control system of claim 1 wherein the active poweralgorithm calculates the maximum active power by: calculating aninductor D-axis voltage drop corresponding to a maximum power gridQ-axis current the inverter can deliver to the power grid; calculatingan inverter Q-axis voltage based on the inverter D-axis voltage and amaximum peak AC voltage of the inverter; calculating a maximum allowableinverter D-axis current based on the inverter Q-axis voltage;calculating a commanded maximum inverter D-axis current based on themaximum allowable inverter D-axis current, the maximum power grid Q-axiscurrent the inverter can deliver to the power grid, and an AC-sidecurrent limit of the inverter; calculating a maximum allowable powergrid D-axis current for delivery to the power grid based on the voltageof the power grid and a DC-side current limit of the inverter;calculating a maximum power grid D-axis current the inverter can deliverto the power grid based on the commanded maximum inverter D-axis currentand the maximum allowable power grid D-axis current; and calculating themaximum active power based on the maximum power grid D-axis current. 7.The control system of claim 6 wherein the active power algorithm setsthe maximum power grid D-axis current equal to the lesser of thecommanded maximum inverter D-axis current and the maximum allowablepower grid D-axis current.
 8. The control system of claim 6 wherein theactive power algorithm calculates the command maximum inverter D-axiscurrent according to:I _(L) _(_) _(d) _(_) _(cmd) _(_) _(max)=min(√{square root over(((kref·1.414·I _(ac) _(_) _(lim))² −I _(grid) _(_) _(q) _(_)_(delivered) ²))},I _(L) _(_) _(d) _(_) _(max)), wherein kref is areference constant corresponding to the representation of D-axis andQ-axis currents and voltages, I_(ac) _(_) _(lim) is the AC current limitof the inverter, I_(grid) _(_) _(q) _(_) _(delivered) is the maximumpower grid Q-axis current the inverter can deliver to the power grid,and I_(L) _(_) _(d) _(_) _(max) is the maximum allowable power gridD-axis current for delivery to the grid.
 9. A method for controlling aninverter comprising: receiving a reactive power command from a utility;sensing a voltage of the power grid and a direct current (DC) voltage ofa power source providing power to the power grid; calculating in areactive power algorithm a maximum reactive power the inverter candeliver to the power grid based on the reactive power command, thevoltage of the power grid, and the DC voltage of the power source;calculating in an active power algorithm a maximum active power theinverter can deliver to the power grid based on the reactive power theinverter can deliver to the power grid; outputting the maximum reactivepower to an inverter current control block; and outputting controlsignals from the inverter current control block to switches of theinverter to control the inverter to output to the power grid the maximumreactive power.
 10. The method of claim 9 further comprising: receivingin the active power algorithm a maximum power point tracking activepower command for the inverter; calculating in the active poweralgorithm an active power for delivery to the power grid based on themaximum active power the inverter can deliver to the power grid and themaximum power point tracking active power command; outputting the activepower for delivery to the power grid to the inverter current controlblock; and outputting control signals from the inverter current controlblock to switches of the inverter to control the inverter to output tothe power grid the active power for delivery to the power grid.
 11. Themethod of claim 9 further comprising: converting the maximum reactivepower the inverter can deliver to the power grid to a Q-axis referencecurrent using the reactive power algorithm; converting the maximumactive power the inverter can deliver to the power grid to a D-axisreference current using the active power algorithm; outputting theQ-axis and D-axis reference currents to the inverter current controlblock; and outputting control signals from the inverter current controlblock to switches of the inverter to control the inverter based on theQ-axis and D-axis reference currents.
 12. The method of claim 9 furthercomprising: limiting the maximum reactive power the inverter can deliverto the power grid based on an AC-side current limit of the inverter; andlimiting the maximum active power the inverter can deliver to the powergrid based on the AC-side current limit of the inverter and a DC-sidecurrent limit of the inverter.
 13. The method of claim 9 furthercomprising limiting the maximum reactive power the inverter can deliverto the power grid and the maximum active power the inverter can deliverto the power grid based on a preset safety factor.
 14. A photovoltaic(PV) system comprising: a PV array; an inverter coupled to the PV arrayfor converting a direct current (DC) voltage of the PV array to analternating current (AC) voltage for delivery to a power grid; a powergrid sensor system for monitoring a voltage of the power grid; a PVsensor for monitoring the DC voltage of the PV array; and a controllerprogrammed to: calculate a maximum reactive power the inverter candeliver to the power grid based on a reactive power command receivedfrom a utility, the voltage of the power grid, the DC voltage of the PVarray, and an AC-side current limit of the inverter; calculate a maximumactive power the inverter can deliver to the power grid based on themaximum Q-axis current and the AC-side current limit of the inverter;and control the inverter to output to the power grid the maximumreactive power and an active power equal to the lesser of the maximumactive power and a maximum power point tracking active power command.15. The PV system of claim 14 wherein the controller is furtherprogrammed to calculate the maximum active power based on a DC-sidecurrent limit of the inverter.
 16. The PV system of claim 14 wherein thecontroller is further programmed to calculate the maximum reactive powerand the maximum active power using three phase representations of D-axisand Q-axis voltages and currents.
 17. The PV system of claim 14 whereinthe controller is further programmed to control the inverter to curtailthe maximum active power when the PV array DC voltage is too low tosupply both the maximum reactive power and the maximum active power tothe power grid.
 18. The PV system of claim 14 wherein the controller isfurther programmed to: convert the maximum reactive power to a Q-axisreference current; convert the maximum active power to a D-axisreference current; and control the inverter based on the Q-axisreference current and the D-axis reference current.
 19. The PV system ofclaim 14 wherein the controller is further programmed to calculate themaximum reactive power based on a maximum peak AC voltage of theinverter, V_(invpeak) _(_) _(max), wherein${V_{invpeak\_ max} = {{ksf} \cdot {kpwm} \cdot \frac{V_{dc}}{2}}},$ andwherein ksf is a safety factor, kpwm is a percentage increase in voltageachieved due to third harmonic injection, and V_(dc) is the DC voltageof the PV array.
 20. The PV system of claim 19 wherein the safety factoris equal to a value within a range from 0.980 to 0.999.